Extension properties and boundary estimates for a fractional heat operator

The square root of the heat operator ∂t−Δ, can be realized as the Dirichlet to Neumann map of the heat extension of data on Rn+1 to R+n+2. In this note we obtain similar characterizations for general fractional powers of the heat operator, (∂t−Δ)s, s∈(0,1). Using the characterizations we derive prop...

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Bibliographic Details
Published inNonlinear analysis Vol. 140; pp. 29 - 37
Main Authors Nyström, K., Sande, O.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2016
Subjects
Boundaries
Boundary Harnack inequality
Dirichlet problem
Dirichlet to Neumann map
Estimates
Fractional heat equation
Fractional Laplacian
Linear degenerate parabolic equation
Lipschitz domain
Mathematical analysis
Nonlinearity
Operators
Parabolic integro-differential equations
Roots
Lipschitz domain
Parabolic integro-differential equations
Linear degenerate parabolic equation
Fractional heat equation
Fractional Laplacian
Dirichlet to Neumann map
Boundary Harnack inequality
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Summary:The square root of the heat operator ∂t−Δ, can be realized as the Dirichlet to Neumann map of the heat extension of data on Rn+1 to R+n+2. In this note we obtain similar characterizations for general fractional powers of the heat operator, (∂t−Δ)s, s∈(0,1). Using the characterizations we derive properties and boundary estimates for parabolic integro-differential equations from purely local arguments in the extension problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0362-546X
1873-5215
1873-5215
DOI:10.1016/j.na.2016.02.027